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What are the domain, range, and asymptote of h(x) = (1.4)^x + 5?

A. domain: {x | x is a real number}; range: {y | y > 5}; asymptote: y = 5
B. domain: {x | x > 5}; range: {y | y is a real number}; asymptote: y = 5
C. domain: {x | x > –5}; range: {y | y is a real number}; asymptote: y = –5
D. domain: {x | x is a real number}; range: {y | y > –5}; asymptote: y = –5

Respuesta :

LammettHash
[tex](1.4)^x[/tex] is always positive for any real [tex]x[/tex], so by itself the range would be [tex]y>0[/tex], but [tex](1.4)^x+5[/tex] adds 5 to every number in that original range. This means the actual range would be all positive numbers greater than 5, or [tex]\{y~|~y>5\}[/tex].

Conveniently, only (B) has this as an option for the range, so this must be the answer. (The other two properties check out, since [tex]x[/tex] can indeed be any real number, while [tex]\displaystyle\lim_{x\to\-\infty}h(x)=5[/tex], so [tex]y=5[/tex] is indeed a horizontal asymptote of [tex]h(x)[/tex].)

Using exponential function concepts, it is found that the correct option that gives the domain, range, and asymptote of h(x) is:

A. domain: {x | x is a real number}; range: {y | y > 5}; asymptote: y = 5

What is an exponential function?

An exponential function is modeled by:

[tex]y = b^x + c[/tex]

  • The domain is all real numbers.
  • The range is y > c.
  • The asymptote is y = c.

In this problem, the function is:

[tex]y = (1.4)^x + 5[/tex]

Hence c = 5, and the option A is correct.

You can learn more about exponential function concepts at https://brainly.com/question/25537936

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